The Viking Age (800-1066) is the most famous period of Scandinavian history. At that time, the Norse seafarers took control of all the sea passages around northern and western Europe, as well the water trade routes in the east and southwards to Russia. They even went as far south as the Mediterranean Sea. On their voyages around the oceans, they discovered and settled uninhabited islands, among them Iceland, the Faroe Islands and Greenland.

Norse Origins
In The Book of the Icelanders (Íslendingabók), the first Icelandic historian, Ari Þorgilsson the Wise (1068-1148), relates the following:

Iceland was first settled out of Norway […] at the time […] when Ivar Ragnarsson Shaggy Breek killed the English King Edmund the Holy. That was seventy winters into the nine hundredth year after the birth of Christ, as described in his saga. There was a Norseman called Ingólfr, who can truly be said to have first travelled to Iceland when Haraldr the Fairhaired was sixteen winters old and a second time a few winters later. He settled in the south, in Reykjavík. (the Icelandic version of Íslendingabók which can be found in Volume 1 of the Íslenzk Fornrit series, this excerpt on pages 4-5.)

There are reports of seafarers who came to the island before Ingólfur’s voyage and who stayed there over the winter. One of these was Flóki Vilgerðarson, also known as “Hrafna-Flóki” or Raven-Floki. He was a Norwegian viking who used the raven as his sailing guide, on account of which he acquired his nickname. He had intended to settle in Iceland but returned to Norway after a difficult winter. It was Hrafna-Flóki who gave Iceland its name.
According to The Book of Settlements (Landnámabók), Ingólfur Arnarson established himself in Iceland in 874. However, it is the Irish monks who are thought to have been the first men to settle the country in the eighth and ninth centuries, although there are few remains or remnants of their settlement. Most indications are that the majority of settlers came from Norway, but there is also talk of the mixing of Norse and Celtic blood when the Norsemen went on Viking raids.
Place names throughout the country bear witness to the Norse origins of the Icelandic people, and some places are named after the Norse gods, such as Þórshöfn (Thor’s harbour) and Þórsmörk (Thor’s pasture), while other place names point to the nation’s Celtic origins, for instance Bekansstaðir (Beecan’s place), Njálsstaðir (Nial’s place) and Írafell (Mount Irish).

Genetic Research into Icelandic Origins
Not everyone is as convinced of the supposed Norse origins of the Icelandic people, and some believe that recent research into the genetics of men on the one hand and women on the other lends support to their doubts. The research has concentrated on genetic mitochondria which are inherited in the female line alone, from mother to child. Since almost all of the inherited genetic mitochondrion of Icelanders has been passed directly from women of the settlement period, it is possible through comparative research to work out their origins.
The first results to come out of the research, which is one of the most extensive genetic research projects ever conducted in one country in order to investigate its origins, and done by DeCode in collaboration with the University of Oxford, indicate that 63% of Icelandic female settlers were of Celtic origin and had ancestral lines traceable to the British Isles. On the other hand, only about 37% of them were of Nordic origins. However, the research into male Y-chromosomes (inherited via the male line) revealed that a much greater percentage of male settlers were of Nordic origins, or 80%, and 20% have origins which can be traced to the British Isles.